Integrate along the given axis using the composite trapezoidal rule.
JAX implementation of numpy.trapezoid()
The trapezoidal rule approximates the integral under a curve by summing the areas of trapezoids formed between adjacent data points.
y (ArrayLike) – array of data to integrate.
x (ArrayLike | None) – optional array of sample points corresponding to the y values. If not provided, x defaults to equally spaced with spacing given by dx.
dx (ArrayLike) – The spacing between sample points when x is None (default: 1.0).
axis (int) – The axis along which to integrate (default: -1)
The definite integral approximated by the trapezoidal rule.
Examples
Integrate over a regular grid, with spacing 1.0:
>>> y = jnp.array([1, 2, 3, 2, 3, 2, 1]) >>> jnp.trapezoid(y, dx=1.0) Array(13., dtype=float32)
Integrate over an irregular grid:
>>> x = jnp.array([0, 2, 5, 7, 10, 15, 20]) >>> jnp.trapezoid(y, x) Array(43., dtype=float32)
Approximate \(\int_0^{2\pi} \sin^2(x)dx\), which equals \(\pi\):
>>> x = jnp.linspace(0, 2 * jnp.pi, 1000) >>> y = jnp.sin(x) ** 2 >>> result = jnp.trapezoid(y, x) >>> jnp.allclose(result, jnp.pi) Array(True, dtype=bool)
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